An approximation algorithm with absolute worst-case performance ratio 2 for two-dimensional vector packing

Authors:
Hans Kellerer;Vladimir Kotov
Affiliations:
Institut für Statistik und Operations Research, Universität Graz, Universitätsstraíe 15, A-8010 Graz, Austria;Faculty of Applied Mathematics and Computer Science, Byelorussian State University, Minsk 220050, Byelorussia
Venue:
Operations Research Letters
Year:
2003

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Abstract

The two-dimensional vector packing problem is the generalization of the classical one-dimensional bin packing problem to two dimensions. While an asymptotic polynomial time approximation scheme has been designed for one-dimensional bin packing, the existence of an asymptotic polynomial time approximation scheme for two dimensions would imply P=NP. The existence of an approximation algorithm for the two-dimensional vector packing problem with an asymptotic performance guarantee 2 was an open problem so far. In this paper we present an O(nlogn) time algorithm for two-dimensional vector packing with absolute performance guarantee 2.